There are obvious differences between a real atmosphere and the simulator atmosphere. A real atmosphere has many more elements to it that create a more complex temperature profile (changes in temperature with changes in height).
Here we compare the atmosphere of Earth with the simulator.
Earth
The Earth's atmosphere is split roughly into four layers. The Troposphere, the Stratosphere, the Mesosphere and the Thermosphere.
The Troposphere contains the bulk of the atmospheric mass and most of the water vapour. The temperature and the amount of water vapour in the Troposphere decreases with height.
The same is true for pressure, which is at it's greatest at the surface.
The Stratosphere is the next layer above the Troposphere. The Stratosphere is actually warmer at the top than the bottom. Ozone at the top of the Stratosphere absorbs UV light and breaks down into O and O2, these then recombine producing heat. Since most of the UV light is absorbed higher up in the Stratosphere, less UV reaches lower down, resulting in lower temperatures in the lower regions of the Stratosphere.
The Mesosphere is above the Stratosphere and reverses the temperature profile again, resulting in cooling with height. At this level in the atmosphere CO2 enables cooling, radiating energy away from the Earth.
The Thermosphere sits above the Mesosphere. In this layer temperature increases again due to energetic solar radiation absorbed by the tiny amounts of oxygen at this altitude. It should be noted that the International Space Station orbits the Earth in the Thermosphere, this demonstrates how thin the atmosphere is at that height.
Simulator
The simulator is a simple representation of an atmosphere that consists of a greenhouse gas and doesn't take into account atmospheric pressure. This results in a relatively linear temperature profile similar to the temperature profile of Earth's Troposphere.
The Stratosphere and Mesosphere atmosphere layers in the simulator are effectively squeezed into the top of the atmosphere, where the greenhouse gases radiate energy to space.
The other clear difference is the absence of Ozone in the Stratosphere and the upper atmosphere interactions with incoming solar energy such as Ultra Violet light.
The simulator currently only takes into account the visible light from the Sun, it is this electromagnetic radiation that penetrates the upper atmosphere, through the Troposphere, warming the surface.